Radio communication, with carrier frequencies of under 100 Mhz, and wire line communication systems are commonly understood to be limited by impulse noise effects rather than the effects of white gaussian types of noise. Impulse noise is introduced into communication channels from man made sources (e.g. ignition or relay contact sparking) or from atmospheric discharges (lightning) or other natural sources. The nature of impulse noise is such that the noise energy occurs in short time intervals with lesser or no noise energy between these discrete events. A different short interval disturbance in magnetic recording of data is known as pulse "drop out" and can be related to impure or absent recording material in small areas of the recording tape, disk or drum.
The technical literature of electronic communications includes several suggestions that data communications improvements could be effected by signal smearing-desmearing techniques for use on impulse noise affected channels. Such smearing-desmearing signal processing techniques are understood to be linear and reversible signal transforms which, by smearing (distributing the desired signal constituents broadly in time) before transmission and subsequently reassembling them at the receiving point, do no harm to the form and detectability of such desired signals. Impulses of noise, on the other hand, would not be influenced by the original smearing process, because of their normal introduction along the transmission path. At the reception point the desmearing process would spread the constituents of the noise impulses, to reduce their additive effect at any one point in time, as it "undid" the spreading of the desired signals. Carrying such an approach to its limit would distribute the impulse noise power uniformly, in time, and reduce impulse noise effects to the more manageable equivalent of a white gaussian noise of the same relative power. Use of such smearing-desmearing techniques would also help minimize phase jitter or very rapid fading effects of the communication path to the extent that the smeared signal would bridge across the disturbance and permit desmearing to reconstitute much of the original signal form. Recording pulse drop out would be alleviated by equivalent smearing-desmearing signal processing for the minimization of errors in recorded data.
Two generic approaches to the linear and reversible smearing-desmearing signal transformation are known. The all pass filter method provides for differing amounts of phase shift, or delay, at different frequencies within the spectrum of interest. The creation of such filter functions, and their inverse, is both a matter of design ingenuity and manufacturing complexity, with consequent expense. The alternative approach can be visualized in terms of a coding-decoding transformation carried out continuously or, on signal samples. The success of such coding methods is dependent on the amount of residual interference, from sample to sample, that results from imperfections in the coding-decoding process. One effect of the coding process is also to introduce different amounts of phase shift (or delay) at different frequencies (of the spectrum of interest) and to reversibly correct these effects in the decoder. It can be shown that the overall process of coding-decoding cannot be perfect, but highly useful resuls can be achieved.
Most work that has been done in coding has been limited to binary sequences. In the domain of binary coding, the "Barker sequences" have been called "perfect" and are provably the best binary codes for the coding-decoding type of smearing-desmearing protection against impulse noise effects on data communication. A full discussion of Barker sequences is found in the text "Radar Signals, An Introduction to Theory and Application" by C. E. Cook and M. Bernfield, Academic Press, New York, 1967, pp. 245 et sq. The use of such Barker sequences, which are purely two-level-integer related sequences, i.e. purely binary in nature, as effective codes for use in smearing-desmearing application is discussed below. In the subsequent discussions, a sampled signal interpretation will be utilized, but equivalent analysis of continuous waveforms would yield very similar conclusions.
A Barker code (or sequence) such as 1,1,1,0,1 will be interpreted as a signal of unit amplitude in successive time positions (chips) but having an inverted (negative) polarity in the fourth such position, in the five long sequence. A Barker coder can be defined as a device having an operation such that, when a single unit amplitude input signal is entered, the device will produce the sequence as an output signal, providing that the input signal duration is just equal to one chip of the output sequence. Such a device might be a lossless delay line with five taps equispaced along it, with these taps feeding a non-loading summing amplifier, and with the fourth tap output being inverted. If the taps were spaced, say, 1 microsecond apart on the delay line, the entering of a 1 volt pulse of 1 microsecond duration could generate, out of the summing amplifier, a voltage sequence of 1,1,1,-1,1 covering a total of 5 microseconds duration and being a representation of the code 1,1,1,0,1. A decoder for this code (or sequence) can be visualized as another tapped delay line in which the time inverse weighting, namely 1,0,1,1,1 is utilized. This is to be interpreted as meaning that the second tap output is inverted into the summing circuit. If the previous Barker sequence (1,1,1-1,1) is then entered into the decoder, an output of 1,0,1,0,5,0,1,0,1 will obtain, where such output values are in units of amplitude and "0" means no amplitude (rather than a signal inversion). This output will be called the autocorrelation function for the sequence 1,1,1,-1,1. The output "5" will be called the autocorrelation peak, while the 1's existing in other positions will be called "hash". Thus, the code can be said to have a peak to (worst) hash ratio (P/H) of 5:1. It can also be noted that it has a peak to sum of the hash (P/.SIGMA. hash) ratio of 5:4. Though all of the above notation has considered unit amplitude signals, the coder and decoder can be linear and would correspondingly scale all amplitudes accordingly. The P/.SIGMA. hash ratio may be considered a measure of intersymbol interference in the following discussion.
If an input sequence 1,1 were entered into the coder (each symbol lasting for 1 microsecond) then the output would be the summation of the independently generated inputs, with a time (position shift) accounting for sequence position. Thus: ##EQU1## being generated at the output of the coder. Similarly, if code 1,0,1 is entered into the encoder and the encoder output is then fed to the decoder, a composite decoder output consisting of the sum of the individual signal outputs is obtained. ##EQU2## Note that the negative of the correlation function is used here for the inverse "0" portion of the input code. The 6,-5,6 portion of the output corresponds to the separate correlation peaks for the 1,0,1 input, but the hash effects are large because they have added in the composite. Indeed, if a longer composite signal were generated, from a longer input sequence, the correlation peaks would be very significantly perturbed from the original value of 5. Such perturbation of the peak seriously interferes with detectability of these peaks, especially in the presence of additive noise effects. As such, the Barker sequences cannot be considered as very useful for this mode of data communication. Additionally, the numbers of available Barker sequences is very limited, and there are none longer than thirteen terms.
The above difficulties with even the "perfect" binary codes have led to investigation of non-binary signals with the goal of complete suppression of all hash, except for some irreducibly small effects at the beginning and end of the autocorrelation function. Where freedom of amplitude and partial phase freedom is permitted, such hash suppressed codes are called Impulse Equivalent Codes. The use of such codes is described in the article "The Generation of Impulse-Equivalent Pulse Trains", D. A. Huffman, IREE Transactions on Information Theory, Vol. II-8, 1962, pp. 510-516. The techniques available for the discovery of such codes are only slightly developed and have led to only a few examples; these suffer from non-uniform time distribution of the signal energy.
Efforts at improving on the Impulse Equivalent Codes have produced the Strictly Complex Impulse Equivalent Codes which utilize the complete freedom of variable phase between elements of the code sequence. Such codes are described in the article "Strictly Complex Impulse-Equivalent Codes and Subsets With Very Uniform Amplitude Distribution", J. R. Caprio, IREE Transactions on Information Theory, Vol. IT-15, 1969, pp. 695-706. These provide an improved distribution of signal energy, at the expense of considerable added complexity and costs.